Please allow me to pull a switcheroo on a well-known phrase:
"If we are to have war, we must prepare for peace."
So maybe we can pummel the Aztecs into eventually giving us a few good techs....is that a strategy we can use throughout the entire game? Even with the Aztecs out of the picture, our two neighbors will then be the Americans and the Japanese - two of the most confident and sprawling empires in the game. I can almost guarantee that both counties already have at least 10-12 cities which means that even a moderately successful Fanatikan campaign will not be conceded readily by either nation. That is not good news for our infrastructure.
We need to define what our borders should be(by settling our perimeters) rather than have them defined for us by our overly-ambitious neighbors. Then we need to build the necessary temples, libaries, granaries and workers to ensure that our cities grow to allow more production which in turn can build us more military support. Only then can we even think of taking on either America or Japan.
Cliff notes version: Weaken or finish Aztecs, build thru to AD, see what happens.... I prefer peace for now.